Evaluate the line integral f. F. dr where F = (2 sin a,–5 cos y, 10xz) and C is the path given by r(t) = (-t³, 2t², 2t) for 0

Q: 1. Calculate the line integral f F-d7, where F (z. y, 2) = -y? +z3 +zk and C is the path C along the…

A: This is a problem from line integral.

Q: Evaluate the line integral F· dr where F (3 sin z, -5 cos y, 5cz) and C is the path given by r(t) =…

A: Line integral is integral of some function along a curve or path. Any field for which the line…

Q: Evaluate the line integral , F. dr where F = (-4 sin x, –3 cos y, 10xz) and C i: the path given by…

A: Given that F→=-4sinx, -3cosy, 10xz and C is the path given by r→t=2t3, t2, -2t for 0≤t≤1 We have to…

Q: Use Green's Theorem to evaluate the line integral |(v - x)dx + (2x – v)dy for the given path. C: x =…

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Q: Evaluate the line integral I of the one-form w = xy dx + 12y dy over the parametric curve a : [0,…

A: Given: One-form ω=xydx+12ydy and the parametric curve α:0, ln2→ℝ2 defined by α(t)=e2t, e-2t. To…

Q: The integral ∫C[(3x2y+y2)dx+(x3+2xy)dy] is independent of the path. Evaluate the integral where C is…

A: Given: R=ti+(t2+t-2)j   for 0<=t<=2

Q: Find the line integral ye-xz ds Here, C is the path r(t) = [t,3t,-6t], 0sts In(8) ·

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Q: Compute the line integral Sc 2.xy dx + x² dy along the following curves. (a) C1 along the circle x2…

A: In given question that is a conservative vector field mean exact integration in which intrgration…

Q: Evaluate the line integral , F dr where F (3 sin x, -5 cos y, xz) and C is the path given by r(t) =…

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Q: 3. Evaluate the line integral f. F· dr where F = (ev+ye")i+(xe"+e")j and C is the parameterized…

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Q: 6. Evaluate the line integral (x? + y² )dx – x dy along the curve C: x? + y² =' counterclockwise…

A: Given: ∫c x2+y2 dx- x dy  We have to Evaluate the given line integral along the curve C: x2+y2=1…

Q: Compute the line integral f 2xy dx + x2 dy along the following curves. (a) C1 along the circle x2 +…

A: A detailed solution is given in steps 2 and 3.

Q: Use Green's Theorem to evaluate the integral (y - x)dx + (2x - y)dy for the given path. C: x = 2…

A: Definition used -                                According to the green theorem -…

Q: Evaluate the line integral by the two following methods. xy dx + x?y3 dy Cis counterclockwise around…

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Q: Evaluate the line integral for the given curve C. S-ds, C: r(t)= (t',t*),1<t<2 cy ||

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve.  xy2…

A: Our Aim is to evaluate the line integral along the given positively oriented curve xy2 dx+3x2y dy…

Q: Evaluate the line integral along the given path. I ( 2+ y2 + z² ) ds C: r(t) = sin(t)i + cos(t)j +…

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Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t > 0. COS So r(t)dt Compute the integral above.

A: ∫0πr(t)dt=∫0π&lt;t,3cos t,3sin t&gt;dt               =∫0πtdt i+∫0π3cos tdt j+∫0π3sintdt k…

Q: Evaluate the line integral along the given path. C: r(t) = sin(t)i + cos(t)j + 3k osts 8

A: The given line integral is ∫Cx2+y2+z2 ds where c is a curve rt=sinti+costj+3k  and  0≤t≤π8.…

Q: Evaluate the line integral | F•ds where F = 2xyi + (x – y²)j and C is (a) y = x from (0,0) to (1,1)…

A: For the solution follow the next steps.

Q: (a) Verify that the Fundamental Theorem for Line Integrals can be used to evaluate the integral Sc…

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Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

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Q: Evaluate the line integral ,F. dr where F = (sin x, –2 cos y, 5xz) and C is the path given %3D by…

A: Integral F.dr = integral F(r(t)).r'(t) dt

Q: Evaluate the line integral (cos x + sin y) ds; C is the line segment from (0, 0) to (x, 67).

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Q: Use Green's Theorem to evaluate the line integral Jo (y - x)dx + (2x - y)dy for the given path. C: x…

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Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x – y)dy for the given path. C: x =…

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Q: Consider the following line integral. xy dx + x²y dy, Cis counterclockwise around the triangle with…

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Q: Consider the following line integral. xy dx + xy3 dy, C is counterclockwise around the triangle with…

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Q: Consider the line integral xy dx + xy° dy with C the triangle with vertices (0, 0). (1,0), and (1,…

A: Given, the line integral Where C is the triangle with vertices.

Q: Let w = e" dx + 4x dy + sin(x1³) dz be a one-form on R³. Find the line integral of w going…

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Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

A: Given integral is ∫Cy−xdx+2x−ydy where C:x=2cosθ,y=sinθ,0≤θ≤2π. Green theorem is given by…

Q: Evaluate the line integral I of the one-form w = (y + z) dx + (x + 2) dy + 10z dz over the line…

A: Given: One-form ω=y+zdx+x+zdy+10zdz and the line segment joining 0, 0, 0 and (3, 1, 0). To find:…

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. y10 dx + x6…

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Q: Evaluate the line integral along the given path. (x² + y² + z?) ds C: r(t) = sin(t)i + cos(t)j + 5k…

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Q: Integrate ƒ(x, y, z) =-2x2 + z2 over the circle r(t) = (a cos t)j + (a sin t)k, )  0&lt;=…

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Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

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Q: Evaluate the line integral F. dr, where F (x, y) = (3+2xy) i+ (x² – 3y²) j and C is the curve given…

A: Given problem:-

Q: Calculate the integral ∫C(x2+y2)zds, where the curve C is parameterized by r(t)=(sin3t,cos3t,4t),…

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Q: (b) Let F(x,y) = (e2*y+cos(7x²), xºy^+e>Y³} Use Green's Theorem to set up the line integral F. dr as…

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Q: Find the value of the closed loop integral z3 + sin z -dz (z – i)3 taken around the boundary of the…

A: GIven  ∮z3+sinz(z-i)3dz   To compute this integral we have to use the following theorem. Theorem:…

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy for the given path. C: x =…

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Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. I (a) √(x…

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Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x - y)dy for the given path. C: x =…

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Q: Evaluate the line integral , F. dr where F = (3 sin x, -5 cos y, xz) and C is the path given by r(t)…

A: To determine the value of the integral.

Q: Evaluate the line integral , F. dr where F = (– sin x, –3 cos y, 5xz) and C is the path given by…

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Q: Evaluate the Line Integral through the Path ab in the below Figure. for the F = p cos o a, + z sin o…

A: The general form of a vector valued function in cylindrical coordinates is given by F=F1aρ+F2aϕ+F3az…

Q: Consider the following line integral. xy dx + x?y dy, Cis counterclockwise around the triangle with…

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Q: Evaluate the line integral [F-dš where F = 2xyi + (x – y')j and C is (a) y =x from (0,0) to %3D…

A: For the solution follow the next steps.

Q: Evaluate line integral F. dr, where F(x, y) =(2xy)i + (x²+3)j, and C is the path given by r(t) = t =…

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Q: Evaluate the line integral, where C is the given curve. x sin(y) ds, C is the line segment from (0,…

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